Abstract. In the paper there is discussed a mathematical framework suitable for specificational problems of modern theory of databases. The main thesis is that a proper framework for a majority of hot problems should be built on the ground of graph-based logic and algebra as opposed to string-based logics and algebras over sets currently employed in the DB theory. Such a graph-based machinery was developed in the mathematical category theory so that the latter can provide a proper foundation. The general problem of building the categorial framework for the DB theory is decomposed into a sequence of special tasks.
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